System and method for designing electromagnetic navigation antenna assemblies

ABSTRACT

A computer-implemented method of designing an antenna assembly for radiating an electromagnetic field for electromagnetic navigation is provided. Multiple diagonal lines are computed, relative to a coordinate system of a substrate having a boundary, based on a seed rectangle having multiple vertices. Each diagonal line bisects a respective vertex of the seed rectangle, and extends from that vertex to the boundary. For each diagonal line, distances between adjacent pairs of planar antenna vertices to be positioned along the respective diagonal line are determined, and the planar antenna vertices are positioned along the respective diagonal line based on the determined distances. The distances increase in a direction from the respective vertex of the seed rectangle to the boundary. A planar antenna layout is generated by interconnecting the planar antenna vertices by way of respective straight linear portions to form multiple loops that sequentially traverse each of the diagonal lines.

BACKGROUND Technical Field

The present disclosure relates to antenna assemblies for electromagnetic navigation and methods for designing such antenna assemblies. More particularly, the present disclosure relates to antenna assemblies for radiating electromagnetic fields for electromagnetic navigation, electromagnetic navigation systems including such antenna assemblies, and computer-implemented methods of designing such antenna assemblies.

Discussion of Related Art

Electromagnetic (EM) navigation (EMN) has helped expand medical imaging, diagnosis, prognosis, and treatment capabilities by enabling a location and/or an orientation of a medical device to be accurately determined while the device is within the body of a patient. One example of a medical procedure in which EMN is employed is ELECTROMAGNETIC NAVIGATION BRONCHOSCOPY® (ENB™), which includes a planning phase and a navigation phase. During the planning phase, a computed tomography (CT) scan of the chest of the patient is used to generate a virtual three-dimensional bronchial map of the patient and a planned pathway for the navigation phase. During the navigation phase, an antenna assembly radiates an electromagnetic field throughout the chest of the patient, a practitioner inserts into the airway of the patient an electromagnetic sensor that senses the radiated electromagnetic field, and a computing device determines a location and/or an orientation (e.g., relative to the planned pathway) of the electromagnetic sensor based on characteristics of the sensed electromagnetic field.

To enable accurate determination of sensor location and/or orientation, a detailed mapping of electromagnetic field measurements at respective sensor locations is generated. Generating such a mapping, however, requires taking precise electromagnetic field measurements at many (for example, hundreds of thousands or more) locations within the expected electromagnetic volume, which is a laborious and time-consuming process that, in some cases, requires expensive machines.

The burden of generating electromagnetic field mappings increases in circumstances where multiple antenna assemblies are employed. For example, in order to enable an electromagnetic sensor to reach deeper portions of the body of the patient, and/or remain within the body during subsequent medical procedures without interfering with additional medical devices, it may be desirable to employ a small electromagnetic sensor, such as a single-coil electromagnetic sensor. However, to employ a small electromagnetic sensor for EMN while maintaining the ability to determine multiple (for example, six) degrees of freedom of the sensor, multiple antenna assemblies may be required to increase the number of radiated electromagnetic fields to be sensed. In such a case, the above-noted exhaustive mapping procedure may need to be conducted for each antenna assembly design. Moreover, given potential variations from manufacturing, the mapping procedure may even need to be completed for each instance of a specific antenna assembly design (i.e., each individual antenna assembly manufactured).

Given the foregoing, a need exists for improved electromagnetic navigation antenna assemblies and methods for designing such antenna assemblies.

SUMMARY

According to an aspect of the present disclosure, an antenna assembly for radiating at least one electromagnetic field for electromagnetic navigation is provided. The antenna assembly includes a substrate and a planar antenna including a trace that is deposited on the substrate and arranged in multiple loops. Respective distances between adjacent pairs of the loops increase in a direction from an innermost loop to an outermost loop.

In another aspect of the present disclosure, each of the loops includes multiple straight linear portions and multiple vertices. For example, in some aspects, each of the loops includes four straight linear portions and four vertices.

In a further aspect of the present disclosure, each of the vertices is disposed along one of four diagonal lines that bisect four respective vertices of a seed rectangle corresponding to the planar antenna.

In yet another aspect of the present disclosure, the antenna assembly further includes a connector having at least two terminals, and the trace has two ends that are coupled to the two terminals, respectively.

In another aspect of the present disclosure, the antenna assembly includes multiple planar antennas, and each of the multiple planar antennas includes a respective trace deposited on the substrate and arranged in a respective set of loops. For each of the planar antennas, respective distances between adjacent pairs of the loops of the respective planar antenna increase in a direction from an innermost loop to an outermost loop.

In another aspect of the present disclosure, the substrate includes multiple layers and the planar antenna and each of the multiple planar antennas is deposited on a respective one of the layers.

In another aspect of the present disclosure, each of the planar antennas includes a same number of loops.

In another aspect of the present disclosure, each of the loops includes multiple straight linear portions and multiple vertices.

In another aspect of the present disclosure, the planar antennas have respective centroids, with respect to a plane of the substrate, that are disposed in respective positions that are distinct from one another.

According to another aspect of the present disclosure, an electromagnetic navigation system is provided. The system includes an antenna assembly, an alternating current (AC) current driver that drives the antenna assembly, a catheter, an electromagnetic sensor, a processor, and a memory. The antenna assembly includes a substrate and a planar antenna and is configured to radiate an electromagnetic field. The planar antenna includes a trace deposited on the substrate and arranged in multiple loops. Respective distances between adjacent pairs of the loops increase in a direction from an innermost one of the loops to an outermost one of the loops. The electromagnetic sensor is affixed to the catheter and is configured to receive a signal based on the radiated electromagnetic field. The memory includes instructions that, when executed by the processor, cause the processor to calculate a location and/or an orientation of the electromagnetic sensor based on the received signal.

In another aspect of the present disclosure, each of the loops includes multiple straight linear portions and multiple vertices. For example, in some aspects each of the loops includes four straight linear portions and four vertices.

In a further aspect of the present disclosure, each of the vertices is disposed along one of four diagonal lines that bisect four respective vertices of a seed rectangle corresponding to the planar antenna.

In yet another aspect of the present disclosure, the antenna assembly further includes a connector having at least two terminals, and the trace has two ends that are coupled to the two terminals, respectively.

In another aspect of the present disclosure, the antenna assembly includes multiple planar antennas, each of the planar antennas including a respective trace deposited on the substrate and arranged in a respective set of loops. For each of the planar antennas, respective distances between adjacent pairs of the loops increase in a direction from an innermost one of the loops to an outermost one of the loops of the respective planar antenna.

In another aspect of the present disclosure, the substrate includes multiple layers and each of the planar antennas is deposited on a respective layer of the multiple layers.

In another aspect of the present disclosure, each of the planar antennas includes a same number of loops.

In another aspect of the present disclosure, each of the loops of each of the planar antennas includes multiple straight linear portions and multiple vertices.

In another aspect of the present disclosure, the multiple planar antennas have multiple centroids, respectively, with respect to a plane of the substrate that are disposed in respective positions that are distinct from one another.

According to another aspect of the present disclosure, an antenna assembly for radiating multiple electromagnetic fields for electromagnetic navigation is provided. The antenna assembly includes a substrate and multiple groups of planar antennas. The substrate includes a multiple layers, and each of the planar antennas includes a respective trace that is deposited on a respective layer of the multiple layers and is arranged in a respective number of loops. Each of the groups of planar antennas includes a first planar antenna, a second planar antenna, and a third planar antenna. For each of the groups of planar antennas: (1) an innermost loop of the first planar antenna has a first linear portion and a second linear portion approximately perpendicular to the first linear portion, (2) an innermost loop of the second planar antenna has a first linear portion and a second linear portion approximately perpendicular to the first linear portion and longer than the first linear portion, (3) an innermost loop of the third planar antenna has a first linear portion and a second linear portion approximately perpendicular to the first linear portion and longer than the first linear portion, (4) the first linear portion of the innermost loop of the second planar antenna is approximately parallel to the first linear portion of the innermost loop of the first planar antenna, and (5) the first linear portion of the innermost loop of the third planar antenna is approximately parallel to the second linear portion of the innermost loop of the first planar antenna.

In another aspect of the present disclosure, for each of the planar antennas, respective distances between adjacent loops of the multiple loops increase in a direction from an innermost loop of the multiple loops to an outermost loop of the multiple loops.

In a further aspect of the present disclosure, the respective innermost loops of the first planar antennas of each group are positioned, on the respective layers of the multiple layers, at respective angles that are distinct from one another.

In yet another aspect of the present disclosure, each of the multiple loops includes multiple straight linear portions and multiple vertices.

In another aspect of the present disclosure, for each planar antenna of the multiple planar antennas, each of the multiple vertices is disposed along one of four diagonal lines that bisect four respective vertices of a seed rectangle corresponding to the respective planar antenna of the multiple planar antennas.

In a further aspect of the present disclosure, respective outermost vertices of the multiple vertices of the multiple planar antennas are distanced from an edge of the substrate by not more than a predetermined threshold.

In yet another aspect of the present disclosure, the planar antennas have respective centroids, with respect to a plane of the substrate, that are distinct from one another.

In another aspect of the present disclosure, each of the planar antennas includes a same number of loops.

In a further aspect of the present disclosure, the number of groups of planar antennas is at least three.

In still another aspect of the present disclosure, the antenna assembly further includes a connector having multiple terminals, and each of the respective traces of the multiple planar antennas is coupled to a respective terminal of the multiple terminals.

According to another aspect of the present disclosure, an electromagnetic navigation system is provided that includes an antenna assembly, a catheter, an electromagnetic sensor, a processor, and a memory. The antenna assembly is configured to radiate electromagnetic fields and includes a substrate and multiple groups of planar antennas. The substrate includes multiple layers, and each of the planar antennas includes a respective trace that is deposited on a respective layer of the multiple layers and is arranged in a respective number of loops. Each of the groups of planar antennas includes a first planar antenna, a second planar antenna, and a third planar antenna. For each of the multiple groups of planar antennas: (1) an innermost loop of the first planar antenna has a first linear portion and a second linear portion approximately perpendicular to the first linear portion, (2) an innermost loop of the second planar antenna has a first linear portion and a second linear portion approximately perpendicular to the first linear portion and longer than the first linear portion, (3) an innermost loop of the third planar antenna has a first linear portion and a second linear portion approximately perpendicular to the first linear portion and longer than the first linear portion, (4) the first linear portion of the innermost loop of the second planar antenna is approximately parallel to the first linear portion of the innermost loop of the first planar antenna, and (5) the first linear portion of the innermost loop of the third planar antenna is approximately parallel to the second linear portion of the innermost loop of the first planar antenna. The electromagnetic sensor is affixed to the catheter and is configured to receive one or more signals based on the radiated electromagnetic fields. The memory includes instructions that, when executed by the processor, cause the processor to calculate a location and/or an orientation of the electromagnetic sensor based on the received signal(s).

In another aspect of the present disclosure, for each of the planar antennas, respective distances between adjacent loops of the multiple loops increase in a direction from an innermost loop of the multiple loops to an outermost loop of the multiple loops.

In a further aspect of the present disclosure, the respective innermost loops of the first planar antennas of each group are positioned, on the respective layers of the multiple layers, at respective angles that are distinct from one another.

In yet another aspect of the present disclosure, each of the multiple loops includes multiple straight linear portions and multiple vertices.

In another aspect of the present disclosure, for each planar antenna of the multiple planar antennas, each of the multiple vertices is disposed along one of four diagonal lines that bisect four respective vertices of a seed rectangle corresponding to the respective planar antenna of the multiple planar antennas.

In a further aspect of the present disclosure, respective outermost vertices of the multiple vertices of the multiple planar antennas are distanced from an edge of the substrate by not more than a predetermined threshold.

In yet another aspect of the present disclosure, the multiple planar antennas have multiple respective centroids, with respect to a plane of the substrate, that are distinct from one another.

In another aspect of the present disclosure, each of the planar antennas includes a same number of loops.

In a further aspect of the present disclosure, the number of groups of planar antennas is at least three.

In yet another aspect of the present disclosure, the electromagnetic navigation system further includes a connector that has multiple terminals, and each of the respective traces of the multiple planar antennas is coupled to a respective terminal of the multiple terminals.

According to another aspect of the present disclosure, a computer-implemented method of designing an antenna assembly for radiating an electromagnetic field for electromagnetic navigation is provided. The method includes computing, relative to a coordinate system of a substrate that has a boundary, multiple diagonal lines based on a seed rectangle that has multiple vertices, respectively. The multiple diagonal lines bisect the multiple vertices of the seed rectangle, respectively, and extend from the multiple vertices of the seed rectangle, respectively, to the boundary. The method also includes, for each of the multiple diagonal lines: (1) determining multiple distances between multiple adjacent pairs of planar antenna vertices, respectively, to be positioned along the respective diagonal line, wherein the multiple distances increase in a direction from the respective vertex of the seed rectangle to the boundary, and (2) positioning the planar antenna vertices along the respective diagonal line based on the determined multiple distances. A planar antenna layout is generated by interconnecting the planar antenna vertices by way of respective straight linear portions to form multiple loops that sequentially traverse each of the multiple diagonal lines.

In another aspect of the present disclosure, the multiple distances are determined based at least in part on a predetermined number of loops of the planar antenna.

In a further aspect of the present disclosure, the multiple distances are determined based at least in part on a predetermined minimum spacing between adjacent vertices and/or a predetermined minimum spacing between adjacent traces.

In yet another aspect of the present disclosure, the substrate has multiple layers and the method further includes generating multiple planar antenna layouts corresponding to the multiple layers, respectively.

In another aspect of the present disclosure, the computer-implemented method further includes adding to the planar antenna layout multiple straight linear portions routed from at least two of the planar antenna vertices to a connector location with respect to the coordinate system of the substrate.

In a further aspect of the present disclosure, the computer-implemented method further includes computing, for each of the multiple diagonal lines, a layout distance between the respective vertex of the seed rectangle and the boundary along the respective diagonal line, and the determining of the multiple distances between the multiple pairs of adjacent planar antenna vertices, respectively, is based at least in part on the computed layout distance.

In yet another aspect of the present disclosure, each of the multiple loops includes multiple of the straight linear portions and multiple of the planar antenna vertices.

In another aspect of the present disclosure, an outermost planar antenna vertex of the multiple planar antenna vertices is distanced from the boundary of the substrate by not more than a predetermined threshold.

In a further aspect of the present disclosure, the computer-implemented method further includes exporting data corresponding to the generated planar antenna layout to a circuit board routing tool and/or a circuit board manufacturing tool.

In yet another aspect of the present disclosure, the computer-implemented method further includes exporting data corresponding to the generated planar antenna layout to an electromagnetic simulation tool and simulating, based on the exported data, an electromagnetic field based on superposition of multiple electromagnetic field components from the multiple straight linear portions of the planar antenna layout, respectively.

According to another aspect of the present disclosure, a non-transitory computer-readable medium is provided, which stores instructions that, when executed by a processor, cause the processor to perform a method of designing an antenna assembly for radiating an electromagnetic field for electromagnetic navigation. The method includes computing, relative to a coordinate system of a substrate having a boundary, multiple diagonal lines based on a seed rectangle that has multiple vertices, respectively. The multiple diagonal lines bisect the multiple vertices of the seed rectangle, respectively, and extend from the multiple vertices of the seed rectangle, respectively, to the boundary. The method further includes, for each of the multiple diagonal lines, (1) determining multiple respective distances between multiple adjacent pairs of planar antenna vertices to be positioned along the respective diagonal line, and (2) positioning the planar antenna vertices along the respective diagonal line based on the determined multiple distances. The multiple distances increase in a direction from the respective vertex of the seed rectangle to the boundary. A planar antenna layout is generated by interconnecting the planar antenna vertices by way of respective straight linear portions to form multiple loops that sequentially traverse each of the multiple diagonal lines.

In another aspect of the present disclosure, the multiple distances are determined based at least in part on a predetermined number of loops of the planar antenna.

In a further aspect of the present disclosure, the multiple distances are determined based at least in part on a predetermined minimum spacing between adjacent vertices and/or a predetermined minimum spacing between adjacent traces.

In yet another aspect of the present disclosure, the substrate has multiple layers and the method further includes generating multiple planar antenna layouts that correspond to the multiple layers, respectively.

In another aspect of the present disclosure, the method further includes adding to the planar antenna layout multiple straight linear portions routed from at least two of the planar antenna vertices to a connector location with respect to the coordinate system of the substrate.

In a further aspect of the present disclosure, the method further comprises, for each of the plurality of diagonal lines, computing a layout distance between the respective vertex of the seed rectangle and the boundary along the respective diagonal line, and the determining of the multiple distances between the multiple pairs of adjacent planar antenna vertices, respectively, is based at least in part on the computed layout distance.

In yet another aspect of the present disclosure, each of the multiple loops includes multiple of the straight linear portions and multiple of the planar antenna vertices.

In another aspect of the present disclosure, an outermost planar antenna vertex of the multiple planar antenna vertices is distanced from the boundary of the substrate by not more than a predetermined threshold.

In a further aspect of the present disclosure, the method further includes exporting data corresponding to the generated planar antenna layout to a circuit board routing tool and/or a circuit board manufacturing tool.

In yet another aspect of the present disclosure, the method further includes exporting data corresponding to the generated planar antenna layout to an electromagnetic simulation tool and simulating, based on the exported data, an electromagnetic field based on superposition of multiple electromagnetic field components from the multiple straight linear portions of the planar antenna layout, respectively.

Any of the above aspects and embodiments of the present disclosure may be combined without departing from the scope of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

Objects and features of the presently disclosed systems and methods will become apparent to those of ordinary skill in the art when descriptions of various embodiments are read with reference to the accompanying drawings, of which:

FIG. 1 is a perspective view of an example electromagnetic navigation (EMN) system in accordance with an embodiment of the present disclosure;

FIG. 2 shows an example design of an antenna assembly of the EMN system in accordance with an embodiment of the present disclosure;

FIG. 3 is a flowchart illustrating an example procedure for designing an antenna assembly in accordance with an embodiment of the present disclosure;

FIGS. 4-11 are example graphical representations of certain aspects of the procedure of FIG. 3, in accordance with an embodiment of the present disclosure;

FIG. 12 is an illustration of multiple example antennas that may be designed according to the procedure of FIG. 3, in accordance with an embodiment of the present disclosure;

FIG. 13 shows an example design of a loop antenna layout trace placement, in accordance with an embodiment of the present disclosure; and

FIG. 14 is a block diagram of an example computing device for use in various embodiments of the present disclosure.

DETAILED DESCRIPTION

The present disclosure is directed to antenna assemblies for radiating electromagnetic fields for electromagnetic navigation, electromagnetic navigation systems that include such antenna assemblies, and computer-implemented methods of designing such antenna assemblies. In one example, by virtue of geometrical and other aspects of an antenna assembly herein, the need to generate and employ a detailed electromagnetic field mapping can be avoided by instead enabling an electromagnetic field mapping, theoretically computed based on characteristics of the antenna assembly, to be employed either alone or in conjunction with a more easily generated low-density electromagnetic field mapping obtained from measurements. In other words, the antenna assembly herein can serve as the basis upon which to generate an accurate high-density theoretical electromagnetic field mapping for EMN, without having to use expensive measuring equipment and without having to perform time-consuming and laborious measurements.

In another example, an antenna assembly herein includes on a single substrate multiple planar antennas having characteristics, such as geometries and/or relative locations that are diverse from one another, that enable multiple (for example, six) degrees of freedom of a small electromagnetic sensor, such as a single-coil sensor, to be determined.

In yet another example, an antenna assembly herein includes a trace that is deposited on a layer of a substrate and that forms multiple loops with the spacing between loops and the spacing from a boundary or edge of the substrate that result in efficient use of the available area of the substrate.

In a further example, an automated, or semi-automated, highly reproducible computer-implemented method for designing an antenna assembly is provided herein. An antenna assembly design generated in this manner can be exported into a printed circuit board (PCB) layout software tool to minimize the need for a large amount of manual layout. The antenna assembly design can also be exported into an electromagnetic field simulator software tool to enable the generation of a theoretical electromagnetic field mapping for the antenna assembly.

Detailed embodiments of antenna assemblies, systems incorporating such antenna assemblies, and methods of designing the same are described herein. These detailed embodiments, however, are merely examples of the disclosure, which may be embodied in various forms. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for enabling one skilled in the art to variously employ the present disclosure in virtually any appropriately detailed structure. While the example embodiments described below are directed to the bronchoscopy of a patient's airways, those skilled in the art will recognize that the same or similar assemblies, systems, and methods may also be used in other lumen networks, such as, for example, the vascular, lymphatic, and/or gastrointestinal networks.

FIG. 1 illustrates an example electromagnetic navigation (EMN) system 100 provided in accordance with the present disclosure. In general, the EMN system 100 is configured to identify a location and/or an orientation of a medical device being navigated toward a target location within the patient's body by using, among other things, an antenna assembly that generates one or more electromagnetic fields that are sensed by a sensor affixed to the medical device. In some cases, the EMN system 100 is further configured to augment computed tomography (CT) images, magnetic resonance imaging (MRI) images, and/or fluoroscopic images employed during navigation of the medical device through the patient's body toward a target of interest, such as a deceased portion in a luminal network of the patient's lung.

The EMN system 100 includes a catheter guide assembly 110, a bronchoscope 115, a computing device 120, a monitoring device 130, a patient platform 140 (which may be referred to as an EM board), a tracking device 160, and reference sensors 170. The bronchoscope 115 is operatively coupled to the computing device 120 (by way of the tracking device 160) and the monitoring device 130 via respective wired connections (as shown in FIG. 1) or wireless connections (not shown in FIG. 1).

During a navigation phase of an EMN bronchoscopy procedure, the bronchoscope 115 is inserted into the oral cavity of a patient 150 and captures images of the luminal network of the lung. The catheter guide assembly 110 is inserted into the bronchoscope 115 to access the periphery of the luminal network of the lung of the patient 150. The catheter guide assembly 110 may include a catheter or extended working channel (EWC) 111 with an EM sensor 112 affixed to a portion (for example, a distal portion) of the EWC 111. A locatable guide catheter (LG) may be inserted into the EWC 111 with another EM sensor (not shown in FIG. 1) affixed to a portion (for example, a distal portion) of the LG. The EM sensor 112 affixed to the EWC 111 or the EM sensor affixed to the LG is configured to receive a signal based on an electromagnetic field radiated by the antenna assembly 145, and based upon the received signal, is used to determine a location and/or an orientation of the EWC 111 or the LG during navigation through the luminal network of the lung. Due to the size restriction of the EM sensor 112 relative to the EWC 111 or the LG, in some cases the EM sensor 112 may include only a single coil for receiving one or more EM signals generated by way of an antenna assembly 145 as described in further detail below. However, the number of coils in the EM sensor 112 is not limited to one but may be two, three, or more.

The computing device 120, such as a laptop, desktop, tablet, or other suitable computing device, includes a display 122, one or more processors 124, one or more memories 126, an AC current driver 127 for providing AC current signals to the antenna assembly 145, a network interface controller 128, and one or more input devices 129. The particular configuration of the computing device 120 illustrated in FIG. 1 is provided as an example, but other configurations of the components shown in FIG. 1 as being included in the computing device 120 are also contemplated. In particular, in some embodiments, one or more of the components (122, 124, 126, 127, 128, and/or 129) shown in FIG. 1 as being included in the computing device 120 may instead be separate from the computing device 120 and may be coupled to the computing device 120 and/or to any other component(s) of the system 100 by way of one or more respective wired or wireless path(s) to facilitate the transmission of power and/or data signals throughout the system 100. For example, although not shown in FIG. 1, the AC current driver 127 may, in some example aspects, be separate from the computing device 120 and may be coupled to the antenna assembly 145 and/or coupled to one or more components of the computing device 120, such as the processor 124 and the memory 126, by way of one or more corresponding paths.

In some aspects, the EMN system 100 may also include multiple computing devices 120, wherein the multiple computing devices 120 are employed for planning, treatment, visualization, or helping clinicians in a manner suitable for medical operations. The display 122 may be touch-sensitive and/or voice-activated, enabling the display 122 to serve as both an input device and an output device. The display 122 may display two-dimensional (2D) images or three-dimensional (3D) images, such as a 3D model of a lung, to enable a practitioner to locate and identify a portion of the lung that displays symptoms of lung diseases.

The one or more memories 126 store one or more programs and/or computer-executable instructions that, when executed by the one or more processors 124, cause the one or more processors 124 to perform various functions and/or procedures. For example, the processors 124 may calculate a location and/or an orientation of the EM sensor 112 based on the electromagnetic signal that is radiated by the antenna assembly 145 and received by the EM sensor 112. The processors 124 may also perform image-processing functions to cause the 3D model of the lung to be displayed on the display 122. The processors 124 may also generate one or more electromagnetic signals to be radiated by way of the antenna assembly 145. In some embodiments, the computing device 120 may further include a separate graphic accelerator (not shown in FIG. 1) that performs only the image-processing functions so that the one or more processors 124 may be available for other programs. The one or more memories 126 also store data, such as mapping data for EMN, image data, patients' medical record data, prescription data, and/or data regarding a history of the patient's diseases, and/or other types of data.

The mapping data may link multiple grid points, in a coordinate system of an EM volume in which a medical device (e.g., the EWC 111, the LG, treatment probe, or another surgical device) navigates, to the EM signal characteristics (for example, signal strength) that correspond to the grid points, respectively. In this manner, when the EM sensor 112 senses an EM signal having certain characteristics at a particular grid point, the one or more processors 124 may compare the sensed EM signal characteristics to the EM signal characteristics in the mapping data and determine the location and/or orientation of the EM sensor 112 within the EM volume based on a result of the comparison.

As shown in FIG. 1, the platform 140 is configured to provide a flat surface upon which the patient 150 lies during the EMN navigation procedure. The antenna assembly 145, which may also be referred to as an EM field generating device, is arranged upon the platform 140 or is included as a component of the platform 140. The antenna assembly 145 includes one or more antennas, such as planar loop antennas (not shown in FIG. 1). Example aspects of the antenna assembly 145 are described in further detail below.

With the patient 150 lying upon the platform 140, the one or more processors 124 (or another signal generator not shown in FIG. 1) generate and provide to the antenna(s) of the antenna assembly 145 by way of the AC current driver 127 one or more AC current signals that the antenna(s) convert into one or more respective EM signal(s) and radiate in a manner sufficient to surround a portion of the patient 150. In some aspects, the antenna assembly 145 includes a connector that has at least two terminals, and the trace of the antenna (not shown in FIG. 1) has two ends that are coupled to the two connector terminals, respectively, to form a signal communication path from the one or more processors 145 to the antenna.

Having described an example EMN system 100, reference will now be made to FIG. 2, which is a graphical illustration of an example antenna assembly layout 200 of the antenna assembly 145 of the EMN system 100, according to an embodiment of the present disclosure. The antenna assembly layout 200 includes a substrate 210, such as a printed circuit board (PCB), which is formed of an electrically insulating material and may include one or more layers. The antenna assembly layout 200 also includes multiple planar antennas 220, which are formed of an electrically conductive material, such as a PCB trace, deposited on the substrate 210 and arranged in multiple loops or as a coil. In one example, each of the planar antennas 220 is deposited on a respective one of the layers of the substrate 210. In the example antenna assembly layout 200 of FIG. 2, multiple layers of the substrate 210 are shown simultaneously.

Each of the multiple antennas may be configured to radiate a separate EM field, for example, using frequency division multiplexing and/or time division multiplexing controlled by the processors 124 or by another generator. For example, the antennas, in some aspects, may be configured to radiate multiple EM fields sufficient in number and/or sufficient in diversity of characteristics (such as frequency, time, modulation scheme, and/or the like) to enable a single-coil electromagnetic sensor mounted on the EWC 111, or on any other medical device, to be used to determine the location and/or the orientation of the sensor, the EWC 111, and/or the medical device. The antenna assembly 145 may, for instance, include six to nine or more loop antennas. In some embodiments, for each of the loop antennas, the distances between its adjacent loops increase as the loops become larger. For example, for each of the planar antennas, respective distances between adjacent pairs of loops may increase in a direction from an innermost one of the loops to an outermost one of the loops of the respective planar antenna. In various embodiments, two or more of the loop antennas of the antenna assembly 145 may have a same number of loops, or may have respectively different numbers of loops.

Having described an example antenna assembly layout 200 of an antenna assembly 145 of the EMN system 100, reference will now be made to FIG. 3, which is a flowchart illustrating an example procedure 300 for designing an antenna assembly such as the antenna assembly 145, in accordance with an embodiment of the present disclosure. In various embodiments, the procedure 300 may be fully computer-implemented or partially computer-implemented. Reference will also be made to FIGS. 4 through 13, which are graphical illustrations of certain steps of the procedure 300, in accordance with an embodiment of the present disclosure. The example method 300 of FIG. 3 may be implemented to design an antenna assembly that includes one antenna or an antenna assembly that includes multiple antennas. For illustrative purposes, the present description of the method 300 will be made in the context of designing an antenna assembly that includes multiple antennas. However, although certain aspects of the method 300 will be described only with respect to the design of a single one of the multiple antennas, those aspects of the method 300 apply similarly to the other ones of the multiple antennas.

Before describing the details of the procedure 300, an overview of the procedure 300 will be provided. In general, according to the procedure 300, the design of the antenna assembly is based on a set of design parameters and/or constraints including a number of antennas M of the antenna assembly to be designed, as well as, for each antenna of the antenna assembly, a seed shape for the antenna, a location of a centroid of the seed shape on the substrate upon which the antenna will be manufactured, a number of loops (N) of the antenna, a minimum trace center-to-center spacing (TCCM) for the antenna, and dimensions of an edge or a boundary of the substrate. Locations of antenna vertices of the antenna are determined based on the seed shape. The antenna design then proceeds by interconnecting the antenna vertices by way of straight linear portions, beginning with the innermost antenna vertices and progressing to the outermost antenna vertices, so that the entire antenna forms a coil including a single trace arranged in multiple loops. In an aspect, each loop of the antenna assembly grows from the seed shape toward the boundaries of the substrate and effectively covers most of the available surface area of the substrate layer outside of the seed shape. The two ends of the trace are routed to a connector location to enable the antenna to be coupled to a signal generator.

For antenna assemblies having multiple planar antennas on respective layers of the multiple layer substrate, this general procedure is repeated for each of the antennas. Additionally, data corresponding to the designed antenna layouts can be exported to an electromagnetic field simulation tool for simulating the electromagnetic field (for example, the theoretical electromagnetic field mapping for EMN described above) that the respective antennas would generate based on their particular characteristics. The data corresponding to the designed antenna layouts can also be exported to a PCB manufacturing tool to enable the antenna assembly to be manufactured in an automated manner, in accordance with the designed antenna layouts.

Before describing the details of the procedure 300, reference will be made to FIG. 4 to describe example seed shapes and their characteristics. In particular, FIG. 4 shows examples of nine seed rectangles 401 through 409 of an antenna assembly to be designed according to the procedure 300. Each of the seed rectangles 401 through 409 includes four vertices within the edge 400 of the substrate. The number of seed rectangles, and hence the number of antennas M, shown in the example of FIG. 4 is nine, however, this is for illustrative purposes only and should not be construed as limiting. In other embodiments, the number of seed shapes, and hence the number of antennas M, may be, for example, six, nine, or more. As an example, the square 400 may represent the edge of the substrate, and a boundary (not shown in FIG. 4) that represents the area of the substrate that is available for placement of the antennas may be formed from a square within the x-z plane that is contained within the edge 400 of the substrate and smaller than the edge 400 of the substrate by some predetermined threshold or buffer amount.

In another example, an antenna assembly herein includes on a single substrate (for example, on respective layers of a multiple-layer substrate) multiple planar antennas having characteristics, such as geometries and/or relative locations that are diverse from one another, that enable multiple (for example, six) degrees of freedom of a small electromagnetic sensor, such as a single-coil sensor, to be determined. For instance, as shown in FIG. 4, the nine seed rectangles 401-409 may be grouped in three, with seed rectangles 401-403 being in a first group; seed rectangles 404-406 being in a second group; and seed rectangles 407-409 being in a third group. As shown in FIG. 4, the three seed rectangles in each group have specific geographical relationships with respect to one another. For instance, one seed rectangle is a square (or substantially square-like), and the other two seed rectangles are non-square rectangles and are located near two sides of the square. For example, the seed rectangle 401 is a square, the seed rectangle 402 is located in line with the length of the seed rectangle 401, and the seed rectangle 403 is located in line with the width of the seed rectangle 401. Further, the length of the seed rectangle 402 is longer than the width of the square 401, and is similar to the length of the seed rectangle 401, while the width of the seed rectangle 402 is smaller than the width of the square 401; and the width of the seed rectangle 403 is longer than the length of the square 401 and is similar to the width of the square 401, while the length of the seed rectangle 402 is smaller than the length of the square 401. The seed rectangles 404-406 of the second group and the seed rectangles 407-409 of the third groups also have the similar geometric features as the seed rectangles 401-403 of the first group.

Put differently, for each of multiple groups of planar antennas that may be generated based on the seed rectangles 401-409: an innermost loop of the first planar antenna (for example, corresponding to the seed rectangle 401) has a first linear portion (for example, first linear portion 410) and a second linear portion (for example, second linear portion 411) approximately perpendicular to the first linear portion (for example, first linear portion 410); an innermost loop of the second planar antenna (for example, corresponding to the seed rectangle 402) has a first linear portion (for example, first linear portion 412) and a second linear portion (for example, second linear portion 413) approximately perpendicular to, and longer than, the first linear portion (for example, first linear portion 412); an innermost loop of the third planar antenna (for example, corresponding to the seed rectangle 403) has a first linear portion (for example, first linear portion 414) and a second linear portion (for example, second linear portion 415) approximately perpendicular to, and longer than, the first linear portion (for example first linear portion 414); the first linear portion (for example, first linear portion 412) of the seed rectangle of the innermost loop of the second planar antenna is approximately parallel to the first linear portion (for example, first linear portion 410) of the innermost loop of the first planar antenna; and the first linear portion (for example, first linear portion 414) of the innermost loop of the third planar antenna is approximately parallel to the second linear portion (for example, second linear portion 411) of the innermost loop of the first planar antenna. Although additional reference numbers for the first and second linear portions of the seed rectangles 404-409 (and hence the correspondence planar antennas) are omitted from FIG. 4 for clarity, the seed rectangles 404-406 of the second group and the seed rectangles 407-409 of the third groups each have similar geometric relationships with respect to one another, as those described above in the context of the seed rectangles 401-403 of the first group.

In an aspect, these three groups may be geometrically dispersed from each group within the substrate 210. Dispersion may be accomplished by geometric relationship and/or angular relationship. For example, the respective innermost loops of the planar antennas of each group can be positioned, on the respective layers of the multiple-layer substrate, at respective angles that are distinct from one another. Additionally, the planar antennas, and/or the seed rectangles upon which the planar antennas are based, may have respective centroids (for example represented by circular dots in FIG. 4), relative to a plane of the substrate, that are mutually distinct from one another. Further, the outer boundaries of the first group include all seed rectangles 404-409 of the second and third groups. Also, the seed rectangles 404-409 of the second and third groups are geometrically dispersed within the outer boundaries of the first group.

Further, each group has an angular relationship with respect to the two axes (i.e., the x axis and the z axis). For example, the seed rectangle 401 of the first group is congruent with the two axes, while the seed rectangles 404 and 407 of the second and third groups are angled with respect to the two axes with different angles, respectively. In other words, the smallest angle between the seed rectangle 401 or the square of the first group and the x axis is zero; the smallest angle between the seed rectangle 404 and the x axis is greater than zero but less than the smallest angle between the seed rectangle 407 of the third group and the x axis. However, the relationship among three groups is not limited to the geometric and angular relationships but can be expanded in any readily conceivable way for a person having ordinary skill in the art within the scope of this disclosure.

Four vertices of each of the seed rectangles 401-409 may be provided in a coordinate form (x, z) in the x-z plane. In an aspect, a centroid of each of the seed rectangles 401-409 may also be provided in coordinate form or can be calculated from the four vertices. Dispersion may also be achieved by dispersing the centroids within the substrate 210. In an aspect, centroids of all seed rectangles 401-409 are disposed on the substrate in positions that are distinct from each other.

Referring now to FIG. 3, prior to block 301, a set of design parameters and/or constraints for the first antenna of the antenna assembly to be designed (for example, a seed shape for the antenna, a location of a centroid of the seed shape on a substrate upon which the antenna will be manufactured, a number of loops (N) of the antenna, a minimum trace center-to-center spacing (TCCM) for the antenna, and dimensions of an edge or a boundary of the substrate) are set (not shown in FIG. 3). For illustrative purposes, the seed shapes utilized in the procedure 300 for each antenna are seed rectangles; however, this should not be construed as limiting. Other seed shapes (for example, a seed triangle, a seed pentagon, a seed hexagon, any convex polygon, convex curved shape (e.g., an ellipse, an egg, a circle, etc.), or any other suitable seed shape) are contemplated and can be employed in the procedure 300. In some embodiments, any combination of different seed shapes can be used for the antennas of the antenna assembly, respectively. Each seed shape has multiple vertices. More specifically, each seed rectangle has four vertices.

At block 301, an antenna index i_(antenna) is initialized. For example, i_(antenna) is set equal to 1 to correspond to the first antenna of the multiple (M, where M>1) antennas of the antenna assembly to be designed. As described below, the purpose of the antenna index i_(antenna) is to enable the procedure 300 to be repeated, in the case of antenna assemblies including multiple antennas, for each antenna of the M antennas of the antenna assembly. For instance, in some examples, the substrate has multiple layers (for example, as in a multi-layer PCB) and the method 300 is employed to generate multiple planar antenna layouts corresponding to the antennas to be deposited on corresponding ones of the multiple layers of the substrate.

At block 302, multiple diagonal lines are computed, relative to a coordinate system of the substrate, based on the seed rectangle. In general, the number of diagonal lines computed at block 302 equals the number of vertices of the seed shape. In particular, in the case of the seed rectangle, which has four vertices, four diagonal lines are computed that bisect the four vertices of the seed rectangle, respectively, and extend from the four vertices of the seed rectangle, respectively, to the boundary of the substrate. The boundary of the substrate may be a physical boundary of the substrate, such as an edge of a PCB, or may be a theoretically imposed boundary, such as a boundary offset from the edge of the PCB by a predetermined buffer distance.

In one example, as part of the computing of the multiple diagonal lines performed at block 302, origins for the diagonal lines of each of vertex of the seed rectangle are first calculated, and then vertices of the innermost loop of the antenna (also referred to as seed vertices) are determined based on the seed rectangle. For example, FIG. 5 shows origins 511 and 512 that are calculated for the seed rectangle 405 of FIG. 4. The origins 511 and 512 are bounded by the four vertices 501 through 504 of the seed rectangle 405. In an aspect, one origin may correspond to a single vertex of the seed rectangle, or one origin may correspond to two adjacent vertices. In another aspect, the origins 511 and 512 may be located on the diagonals of the seed rectangle or on the diagonals which bisect the corresponding angle to form two 45 degree angles. In this case, diagonals define the locations of vertices of the loop antenna. As an example, the origin 511 is located on a diagonal, which bisects the 90 degree angle at the vertex 501 to form two 45 degree angles. Also as shown in FIG. 5, the origin 511 is located on the intersection of the diagonals which bisect the angles at vertices 501 and 502. In the same way, the origin 512 is located at the intersection of the diagonals which bisect the angles at vertices 503 and 504. In one example, the origins for the diagonal lines of each vertex of the seed rectangle can be calculated by performing principal component analysis (PCA) over the coordinates of the four vertices 501-504, utilizing singular value decomposition. The following notations are used herein:

-   -   P_(jk) represents the k-th vertex of the j-th loop, where j is 1         to N and k is 1 to 4;     -   P_(jkx) and P_(jkz) represent x-coordinate and z-coordinate of         the vertex P_(jk), respectively;     -   {P_(j1), P_(j2), P_(j3), P_(j4)} or simply {P_(jk)} is a 4 by 2         matrix having four vertices P_(j1), P_(j2), P_(j3), P_(j4) of         the j-th loop as its rows;     -   U represents a 4 by 4 matrix having orthonormal eigenvectors of         {P_(jk)}{P_(jk)}^(T) as its column;     -   V represents a 2 by 2 matrix having orthonormal eigenvectors of         {P_(jk)}^(T){P_(jk)} as its column; and     -   S represents a 4 by 2 matrix, whose nonzero elements are located         only at its diagonal and are square root of eigenvalues of         {P_(jk)}{P_(jk)}^(T) or {P_(jk)}^(T){P_(jk)}; and     -   {tilde over (S)} represents a 4 by 2 matrix, whose nonzero         elements are located only at its diagonal and are equal to the         smallest nonzero element of S.

Given the four vertices R_(k), (R_(kx), R_(kz)), of the i-th seed rectangle, a centroid C, (C_(x), C_(z)), of the i-th seed rectangle is calculated as follows:

$\begin{matrix} {\left( {C_{x},C_{z}} \right) = {\left( {\frac{\sum\limits_{k = 1}^{4}\; R_{kx}}{4},\frac{\sum\limits_{k = 1}^{4}\; R_{kz}}{4}} \right).}} & (1) \end{matrix}$

By performing singular value decomposition on the centroid-subtracted four vertices R_(j), S, V, and D matrices are obtained as follows:

USV ^(T) ={R _(k) −C}  (2),

where {R_(k)−C} is a 4 by 2 matrix, each row of {R_(k)−C} is the centroid-subtracted vertex (R_(kx)−C_(x), R_(kz)−C_(z)), and k is 1 to 4.

S is a 4 by 2 matrix having nonzero elements only in the diagonal, i.e., S₁₁ and S₂₂. Based on the singular value decomposition, S₁₁ is greater than or equal to S₂₂. By replacing the value of S₁₁ with the value of S₂₂, we can get a new 4 by 2 diagonal matrix {tilde over (S)}, where {tilde over (S)}₁₁ and {tilde over (S)}₂₂, are equal to S₂₂. Then, the origins O_(k) for each vertex can be obtained by the following:

{O _(k) }={R _(k) }−U{tilde over (S)}V ^(T)  (3).

Because the diagonal entries of {tilde over (S)} are the minimum values of the diagonal entries of S, {O_(k)} includes only two different rows, corresponding to the origins 511 and 512, within the i-th seed rectangle, as shown in FIG. 5.

After obtaining the origins 511 and 512, a first set of four seed vertices P_(1k) within the i-th seed rectangle are determined. These first four seed vertices P_(1k) are the seed vertices for the innermost loop of the respective antenna and can be used to determine the other vertices of that antenna.

Given the minimum trace center-to-center (TCCM) spacing, which represents a predetermined minimum distance between traces or loops of a particular antenna or of all the antennas of a particular antenna assembly, the first seed vertex P₁₁ is determined by moving R₁ into its corresponding diagonal, which bisects the 90 degree angle at R₁, toward the inside of the i-th seed rectangle. This can be done by first defining two vectors from R₁ as follows:

{right arrow over (V _(R) ₁₄ )}={right arrow over (R ₄)}−{right arrow over (R ₁)}  (4),

{right arrow over (V _(R) ₁₂ )}={right arrow over (R ₂)}−{right arrow over (R ₁)}  (5),

where {right arrow over (R_(k))} is a vector pointing toward R_(k) from the respective origin O_(k), {right arrow over (V_(R) ₁₄ )} is a vector pointing toward R₄ from R₁, and {right arrow over (V_(R) ₁₂ )} is a vector pointing toward R₂ from R₁. By adding the unit vector of

$\overset{\rightarrow}{V_{R_{14}}},\frac{\overset{\rightarrow}{V_{R_{14}}}}{\overset{\rightarrow}{V_{R_{14}}}},$

to the unit vector of

$\overset{\rightarrow}{V_{R_{12}}},\frac{\overset{\rightarrow}{V_{R_{12}}}}{\overset{\rightarrow}{V_{R_{12}}}},$

a vector having a direction in line with the respective diagonal line, which bisects the 90 degree angle at R₁ to form two 45 degree angles, is obtained, where the symbol “∥ ∥” represents a magnitude of the vector inside of the symbol “∥ ∥”. Then, the first seed vertex P₁₁ is obtained by the following equation:

$\begin{matrix} {{\overset{\rightarrow}{P_{11}} = {\overset{\rightarrow}{R_{1}} + {{TCCM} \times \left( {\frac{\overset{\rightarrow}{V_{R_{14}}}}{\overset{\rightarrow}{V_{R_{14}}}} + \frac{\overset{\rightarrow}{V_{R_{12}}}}{\overset{\rightarrow}{V_{R_{12}}}}} \right)}}},} & (6) \end{matrix}$

where {right arrow over (P₁₁)} is a vector originating from the respective origin O₁ and thus represents a coordinate of P₁₁. FIG. 6 illustrates the other three seed vertices P₁₂, P₁₃, and P₁₄ of the antenna, which match R₂, R₃, and R₄. The smallest distance between P_(1k) and the four sides of the i-th seed rectangle equals TCCM. FIG. 7 shows vectors Diag₁, Diag₂, Diag₃, and Diag₄, which may form respective portions of the diagonal lines that bisect the seed vertices P₁₁, P₁₂, P₁₃, and P₁₄ and extend from the respective seed vertices P₁₁, P₁₂, P₁₃, and P₁₄ to the boundary of the substrate.

Referring back to FIG. 3, at block 303 a diagonal line index i_(diagonal) is initialized. For example, i_(diagonal) is set equal to 1 to correspond to the first diagonal line of the four diagonal lines of the seed rectangle. As described below, the purpose of the diagonal line index i_(diagonal) is to enable aspects of the procedure to be repeated for each of the diagonal lines of the seed rectangle.

At block 304, for the respective diagonal line, a vertex-layout-distance (also referred to herein as a layout distance) V_(layout) _(_) _(k) between the respective vertex of the seed rectangle and the boundary of the substrate, along the respective diagonal line is computed. The layout distance may represent, or may be related to, the maximum usable distance between the respective vertex of the seed rectangle and the boundary of the substrate.

In some example embodiments, as part of the computing of the layout distance at block 304, respective intersecting points T_(k) between the origins O_(k) and the boundary of the substrate, when the respective diagonals {right arrow over (Diag_(k))} are projected from the origins O_(k), are calculated and identified, as shown, for example, in FIG. 9. The intersecting points T_(k) can be found using multiple conventional approaches. When the intersecting points T_(k) are found, the following relationship is satisfied:

$\begin{matrix} {{\frac{\overset{\rightarrow}{O_{k}T_{k}}}{\overset{\rightarrow}{O_{k}T_{k}}} = \frac{\overset{\rightarrow}{{Diag}_{k}}}{\overset{\rightarrow}{{Diag}_{k}}}},} & (14) \end{matrix}$

where {right arrow over (O_(k)T_(k))} is a vector from the origin O_(k) to the intersecting point T_(k). In other words, vector {right arrow over (O_(k)T_(k))} has the same direction as the diagonal vector {right arrow over (Diag_(k))}.

With the four vertices P₁₁, P₁₂, P₁₃, and P₁₄ of the first loop and the intersecting points T₁, T₂, T₃, and T₄ identified, the vertex-layout-distance, V_(layout) _(_) _(k), can be calculated from the following equation:

$\begin{matrix} {V_{{layout}\_ k} = {{\overset{\rightarrow}{P_{1\; k}T_{k}}} - {\frac{VVM}{2}.}}} & (15) \end{matrix}$

The subtracting term,

$\frac{VVM}{2},$

ensures that the last vertex P_(Nk) of the N-th loop is distant from the intersecting point T_(k). In other words, only a V_(layout) _(_) _(k)-long linear portion starting from P_(1k) is used to distribute (N−1) vertices between P_(1k) and T_(k).

After the intersecting points T_(k) are identified, every vertex for the loop antenna can be determined. As one of the initial conditions is that the number of loops of the loop antenna is N and the four vertices P₁₁, P₁₂, P₁₃, and P₁₄ of the first loop are determined in step 330, four vertices of each of the second, third, . . . , and N-th loops are recursively determined. In particular, at block 305, for the respective diagonal line, respective distances between adjacent pairs of planar antenna vertices to be positioned along the respective diagonal line are determined based at least in part on the layout distance computed at block 304. For example, the respective distances between adjacent pairs of planar antenna vertices to be positioned along the respective diagonal line may be determined so as to fit the predetermined number of loops N of the antenna while maximizing the use of the available linear distance from the vertex of the seed rectangle to the boundary of the substrate. In this manner, the available area of the substrate may be efficiently utilized. Additionally, in some example aspects, an outermost planar antenna vertex of the planar antenna vertices of the respective planar antenna is distanced from the boundary of the substrate by not more than a predetermined threshold, for efficient utilization of the available substrate area.

In some examples, the respective distances are determined at block 305 based at least in part on the predetermined number N of loops of the planar antenna, a predetermined minimum spacing between adjacent vertices, a predetermined minimum spacing between adjacent traces, and/or any combination of one or more of those factors or other factors. In particular, in one example, vertices are grouped in four groups with each group forming a rectangular shape, and vertices in the same group are described as corresponding vertices. For example, the first group includes P₁₁, P₂₁, . . . , and P_(N1), the second group includes P₁₂, P₂₂, . . . , and P_(N2), the third group includes P₁₃, P₂₃, . . . , and P_(N3), and the fourth group includes P₁₄, P₂₄, . . . , and P_(N4). Thus, P_(3k) and P_(Nk) are in the same k-th group and are corresponding vertices, while P₃₃ and P₄₂ are not in the same group and cannot be corresponding vertices. For each group, the distance between P_(jk) and P_((j+1)k) is set to be greater than the distance between P_((j+1)k) and P_(jk), where j is 2 to N−1 and k is 1 to 4. In other words, the distance between two adjacent corresponding vertices is increasing toward the boundary of the substrate. Put differently, in one example, as illustrated in FIG. 10, the distances between the adjacent pairs of antenna vertices become progressively larger in a direction from an innermost one of the vertices to an outermost one of the vertices. The progressively increasing distance in a direction from the respective vertex of the seed rectangle to the boundary may be implemented by various methods, such as arithmetic progression, geometric progression, exponential progression, and/or the like.

For example, arithmetic progression may be employed to distribute remaining vertices in each group. Letting d_(jk) be the distance between P_(jk) and P_((j+1)k) in the k-th group and be expressed in recursive form as:

∥{right arrow over (P _(jk) P _((j+1)k))}∥=d _(jk)  (16),

d _(jk)=slope_(k)×(j−1)+d _(1k)  (17)

and

d _(1k) =VVM  (18),

where ∥{right arrow over (P_(jk)P_((j+1)k))}∥ represents a distance between vertices P_(jk) and P_((j+1)k), slope_(k) is a constant for the k-th group, which is the common difference between two distances d_(jk) and d_((j+1)k), and j is 1 to (N−2). Thus, each vertex in the k-th group is positioned on the linear portion connecting T_(k) and P_(1k) and the total length between P_(Nk) and P_(1k) is less than or equal to the vertex-layout-distance, V_(layout) _(_) _(k). In order to make an additional keepout area of half the minimum trace center to center (TCCM) spacing between the T_(k) and P_(Nk), the following equation may be satisfied:

$\begin{matrix} {{{\sum\limits_{j = 1}^{N - 1}\; {{P_{jk}P_{{({j + 1})}k}}}} = {V_{{layout}\_ k} - \frac{TCCM}{2}}},{or}} & (19) \\ {{\sum\limits_{j = 1}^{N - 1}d_{jk}} = {{\sum\limits_{j = 1}^{N - 1}\left( {{{slope}_{k} \times \left( {j - 1} \right)} + d_{1\; k}} \right)} = {V_{{layout}\_ k} - {\frac{TCCM}{2}.}}}} & (20) \end{matrix}$

When equation (20) is solved for the constant, slope_(k), the following equation can be obtained:

$\begin{matrix} {{slope}_{k} = {\frac{2 \cdot \left( {V_{{layout}\_ k} - {\left( {N - 1} \right)d_{1\; k}} - \frac{TCCM}{2}} \right)}{\left( {N - 1} \right)\left( {N - 2} \right)}.}} & (21) \end{matrix}$

When the equation (20) is combined with equations (16) and (17), the following equation is obtained:

$\begin{matrix} {{\overset{\rightarrow}{P_{jk}P_{{({j + 1})}k}}} = {{\frac{2 \cdot \left( {V_{{layout}\_ k} - {\left( {N - 1} \right)d_{1\; k}} - \frac{TCCM}{2}} \right)}{\left( {N - 1} \right)\left( {N - 2} \right)}\left( {j - 1} \right)} + {d_{1\; k}.}}} & (22) \end{matrix}$

In this way, the distance between two adjacent corresponding vertices P_(jk) and P_((j+1)k) increases as j increases. This progressive pattern between corresponding vertices is shown in FIG. 10 more clearly in the first and the fourth groups than in the second and the third groups.

At block 306, the planar antenna vertices are positioned along the respective diagonal line based on the respective distances between adjacent pairs of planar antenna vertices determined at block 305.

At block 307, the diagonal line index i_(diagonal) is compared to the number of diagonal lines, namely four, of the seed rectangle to determine whether the procedures of block 305 and block 306 are to be repeated for additional diagonal lines of the respective antenna. If it is determined at block 307 that i_(diagonal) is less than the number of diagonal lines, then at block 308 i_(diagonal) is incremented by one to correspond to the next diagonal line (for example, the second diagonal line) of the four diagonal lines of the seed rectangle. Then the procedures of block 305 and block 306 are repeated for that next diagonal line in the manner described above.

If, on the other hand, it is determined at block 307 that i_(diagonal) is equal to the number of diagonal lines, indicating that the procedures of block 305 and block 306 have been executed for each of the four diagonal lines of the seed rectangle, then at block 309, a minimum vertex to vertex distance (VVM) is calculated to make sure that, when vertices are connected by linear portions or segments of a line, the smallest distance between two adjacent corresponding linear portions is greater than TCCM, where the phrase “two adjacent corresponding linear portions” being used to refer to linear portions that are positioned in different loops but are located closer to one another than any other linear portions. This is done by defining diagonal vectors {right arrow over (Diag_(k))}, setting up temporary vertices P′₂₁ and P′₂₂, measuring a distance between a linear portion connecting the temporary vertices P′₂₁ and P′₂₂ and a linear portion connecting P₁₁ and P₁₂, and adjusting a value of VVM until the smallest distance is greater than TCCM. Details of this step are further described below.

The diagonal vectors {right arrow over (Diag_(k))} are defined as follows:

{right arrow over (Diag_(k))}={right arrow over (P _(1k))}−{right arrow over (O _(k))}  (7),

where k is 1 to 4. When these diagonal vectors {right arrow over (Diag_(k))} are arranged at the origin (0, 0), they form a cross indicating that they form four 90 degree angles as shown in the middle of FIG. 7.

A temporary distance D_(p2to5) is initialized as the value of TCCM. Vectors {right arrow over (V_(P) ₃₂ )}, {right arrow over (P′_(22 temp))}, and {right arrow over (V_(P) ₂₂ _(temp))} are defined by the following:

$\begin{matrix} {{\overset{\rightarrow}{V_{P_{32}}} = {\overset{\rightarrow}{P_{12}} - \overset{\rightarrow}{P_{13}}}},} & (8) \\ {{\overset{\rightarrow}{P_{22\; {temp}}^{\prime}} = {\overset{\rightarrow}{P_{12}} + {D_{p\; 2\; {{to}5}} \times \frac{\overset{\rightarrow}{V_{P_{32}}}}{\overset{\rightarrow}{V_{P_{32}}}}}}},{and}} & (9) \\ {\overset{\rightarrow}{V_{P_{22}{temp}}} = {\overset{\rightarrow}{P_{22\; {temp}}^{\prime}} - {\overset{\rightarrow}{P_{12}}.}}} & (10) \end{matrix}$

Temporary vertex P′₂₂ is defined in a vector form as follows:

$\begin{matrix} {{\overset{\rightarrow}{P_{22\;}^{\prime}} = {\overset{\rightarrow}{P_{12}} + {\frac{\overset{\rightarrow}{{Diag}_{2}}}{\overset{\rightarrow}{{Diag}_{2}}} \times \frac{{\overset{\rightarrow}{V_{P_{22}{temp}}}}^{2}}{\overset{\rightarrow}{V_{P_{22}{temp}}} \cdot \frac{\overset{\rightarrow}{{Diag}_{2}}}{\overset{\rightarrow}{{Diag}_{2}}}}}}},} & (11) \end{matrix}$

where the symbol “⋅” is a dot product between two vectors. In short, temporary vertex P′₂₂ is distant from P₁₂ by √{square root over (2)}×TCCM in a direction of the diagonal {right arrow over (Diag₂)} toward outside of the i-th seed rectangle. Next, VVM is temporarily initialized with the following equation:

VVM=∥{right arrow over (P′ ₂₂)}−{right arrow over (P ₁₂)}∥  (12).

Temporary vertex P′₂₁ is defined in a vector form as follows:

$\begin{matrix} {\overset{\rightarrow}{P_{21\;}^{\prime}} = {\overset{\rightarrow}{P_{11}} + {{VVM} \times {\frac{\overset{\rightarrow}{{Diag}_{1}}}{\overset{\rightarrow}{{Diag}_{1}}}.}}}} & (13) \end{matrix}$

As with P′₂₂, temporary vertex P′₂₁ is distant from P₁₁ by √{square root over (2)}×TCCM in a direction of the diagonal {right arrow over (Diag₁)} toward outside of the i-th seed rectangle.

As shown in FIG. 8, distances between the linear portion connecting temporary vertices P′₂₁ and P′₂₂ and the linear portion between P₁₁ and P₁₂ are calculated. Since the linear portion connecting temporary vertices P′₂₁ and P′₂₂ and the linear portion between P₁₁ and P₁₂ may not be parallel, there are multiple distances between the two linear portions. At block 309, a determination is made as to whether the smallest distance D among the multiple distances between the two linear portions is less than or equal to TCCM. If it is determined at block 309 that the smallest distance D among the multiple distances is less than or equal to TCCM, then at block 311 the temporary distance D_(p2to5) is increased by a predetermined amount and the above procedures of blocks 302 through 309 are repeated, including by using the equations (9)-(13) until the smallest distance D is greater than TCCM. The final result of VVM is set as the value for the vertex-to-vertex minimum.

If, on the other hand, it is determined at block 309 that the smallest distance D among the multiple distances is greater than TCCM, then at block 312 a planar antenna layout is generated by interconnecting the planar antenna vertices by way of respective straight linear portions to form multiple loops (e.g., N loops) that sequentially traverse each of the plurality of diagonal lines of the respective planar antenna. Each of the loops includes multiple straight linear portions and multiple planar antenna vertices, namely four straight linear portions and four planar antenna vertices, in a case where the seed shape is a seed rectangle. For example, the first loop of each loop antenna, such as the loop antenna shown in FIG. 11, includes four vertices (i.e., P₁₁, P₁₂, P₁₃, and P₁₄) and four linear portions (i.e., L₁₁ connecting between P₁₁ and P₁₂, L₁₂ connecting P₁₂ and P₁₃, L₁₃ connecting P₁₃ and P₁₄, and L₁₄ connecting P₁₄ and P₂₁); . . . the (N−1)-th loop includes four vertices (i.e., P_((N-1)1), P_((N-1)2), P_((N-1)3), and P_((N-1)4)) and four linear portions (i.e., L_((N-1)1) connecting between P_((N-1)1) and P_((N-1)2), L_((N-1)2) connecting P_((N-1)2) and P_((N-1)3), L_((N-1)3) connecting P_((N-1)3) and P_((N-1)4), and L_((N-1)4) connecting P_((N-1)4) and P_(N1)) (for clarity, not labeled in FIG. 11); and the N-th loop includes four vertices (i.e., P_(N1), P_(N2), P_(N3), and P_(N4)) and three linear portions (i.e., L_(N1) connecting P_(N1) and P_(N2), L_(N2) connecting P_(N2) and P_(N3), and L_(N3) connecting P_(N3) and P_(N4)). FIG. 11 shows a design for a loop antenna that includes a plurality of loops, which is designed according to the procedure 300.

At block 313, multiple additional straight linear portions are routed from at least two of the planar antenna vertices (in particular, from the two terminal antenna vertices located at the two ends, respectively, of the linear planar antenna layout) to one or more connector locations with respect to the coordinate system of the substrate. The multiple additional straight linear portions are added to the planar antenna layout. In embodiments where the procedure 300 is employed to design an antenna assembly that includes multiple planar antennas to be arranged on respective layers of a multiple-layer substrate, the planar antenna layouts may be routed to a single connector location, or to separate connector locations corresponding to each antenna, respectively, or to any combination of connectors.

At block 314, the antenna index i_(antenna) is compared to the number of antennas M of the antenna assembly to determine whether the procedures of block 302 through block 313 are to be repeated for additional antennas of the antenna assembly. If it is determined at block 314 that i_(antenna) is less than the number of antennas M, then at block 315 i_(antenna) is incremented by one to correspond to the next antenna (for example, the second antenna) of the M antennas of the antenna assembly. Then the procedures of block 302 through block 313 are repeated for that next antenna in the manner described above. FIG. 12 shows designs for six loop antennas, which can be designed in accordance with the procedure 300.

If, on the other hand, it is determined at block 314 that i_(antenna) is equal to the number of antennas M, indicating that the procedures of block 302 through block 313 have been executed for each of the M antennas of the antenna assembly, then at block 316, which may be optional in some embodiments, data corresponding to the generated planar antenna layout is exported to a circuit board routing tool, a circuit board manufacturing tool, and/or an electromagnetic simulation tool.

In one example, by exporting the data corresponding to the generated planar antenna layout to the electromagnetic simulation tool at block 316, one or more electromagnetic fields that may be generated by the antennas of the antenna assembly may be simulated based on the exported data and on the superposition of multiple electromagnetic field components from each of the multiple straight linear portions of the planar antenna layout, respectively. For instance, each loop based on the seed shape can be expressed with a definite mathematical equation, such as a Cartesian equation or a parametric equation, such that the strength of an EM field generated by each loop can be calculated by the Biot-Savart-Laplace law at any point in space based on the mathematical equation. In other words, by virtue of geometrical and other aspects of the antenna assembly (such as the use of straight linear portions as the interconnections in the antennas of the antenna assembly), the need to generate and employ a detailed electromagnetic field mapping can be avoided by instead enabling an electromagnetic field mapping to be theoretically computed based on the characteristics of the antenna assembly. The computed electromagnetic field mapping can then be employed either alone or in conjunction with a more easily generated low-density electromagnetic field mapping obtained from measurements. In other words, the antenna assembly designed according to the procedure 300 can serve as the basis upon which to generate an accurate high-density theoretical electromagnetic field mapping for EMN, without having to use expensive measuring equipment and without having to perform time-consuming and laborious measurements.

As is apparent from the description herein, according to the procedure 300, an antenna assembly can be efficiently and designed in a repeatable manner based on a few design parameters and/or constraints, such as a seed shape, a number of loops, a TCCM, and/or the like. Each of the antennas of the designed antenna assembly can be printed, deposited, or fabricated on a respective substrate layer and can be used as the EM field generator 145 of the EMN system 100 of FIG. 1. Further, by virtue of employing straight linear portions to constitute the loop antennas, electromagnetic fields generated by each linear portion can be theoretically and accurately calculated using the Biot-Savart-Laplace law at any point in the EM volume.

FIG. 13 shows a graphical illustration of a loop antenna layout designed by the method 300 of FIG. 3. After connecting all the vertices, additional layout may be automatically generated based on a few design rules in place related to trace length and routing directionality. These rules may be specific to a PCB software program or design requirements. In an aspect, the antenna design made by the method 300 may be converted to a 2 dimensional DXF (Drawing eXchange Format) CAD file, which is then imported into Altium PCB layout software. PCB layout software is not limited to Altium PCB layout software but can be any software, which a person having ordinary skill in the art would readily appreciate and use.

Based on the design rules or design requirements of the software, vertices P₁₁ and P_(N4) are electrically coupled to a connector 1301, which includes at least two conductors 1301 a, 1301 b of the loop antenna, respectively, and a full blueprint of the loop antenna is complete.

Upon completion of the design of the antenna assembly, an antenna is fabricated, based on the antenna assembly design, by depositing electrically conducting materials (e.g., silver or copper) on a substrate, as shown in FIG. 13. The antenna printed on the substrate includes structural and/or geometrical relationships between loops, which are described in detail below.

In an example aspect, vertices of the loop antenna can be grouped in four groups. The first group of vertices includes P₁₁, P₂₁, . . . , and P_(N1), the second group of vertices includes P₁₂, P₂₂, . . . , and P_(N2), the third group of vertices includes P₁₃, P₂₃, . . . , and P_(N3), and the fourth group of vertices includes P₁₄, P₂₄, . . . , and P_(N4). Because V_(layout) _(_) _(k) is different for each group, one group of vertices may be more densely distributed than the other groups of vertices. As shown in FIG. 13, vertices in the fourth group are more loosely distributed than vertices in the other groups, and the vertices in the second or third group are more densely distributed than vertices in the first and fourth groups.

In another aspect, the shortest distance between two corresponding linear portions (e.g., L_(jk) and L_((j+1)k)) increases as j increases. In other words, the distances between two adjacent corresponding linear portions are increasing in a direction from the innermost linear portion to the corresponding outermost linear portion. Based on this structural and/or geometrical relationship among loops and vertices, the loop antenna can cover the substrate as much as possible while maintaining such a relationship.

In an embodiment, after connecting the vertices with linear portions, another safety measure may be employed to confirm that all the requirements are satisfied in the antenna design. For example, shortest distances between two adjacent corresponding linear portions may be calculated again. In a case when there are any two adjacent corresponding linear portions, between which the shortest distance is not greater than TCCM, the procedure 300 can be repeated with a different minimum vertex to vertex distance VVM.

In an aspect, the design procedure 300 can enable maintaining substantially the same inductance of each loop antenna because the inductance is defined based at least in part on the antenna geometry. The resistance of the loop antenna may vary with copper thickness on each layer. Thus, in order to ensure that the antenna assembly maintains the intended copper thickness, two additional layers (one on the top and the other on the bottom) are added. With these extra layers, the plating processing for the vias would not add copper to the antenna layers on the internal layers. Thus, the copper thickness may depend only on the core material used and copper weight selected, initially. In another aspect, the PCB design may contain more than a single via for each current carrying path to minimize series resistance and increase the robustness of each current path. By having more vias, the resistance can be predicted and automatically calculated with high accuracy based on the antenna geometry and controlled copper thickness.

Turning now to FIG. 14, there is shown a block diagram of a computing device 1400, which can be used as the EMN system 100, the control workstation 102, the tracking device 160, and/or a computer performing the procedure 300 of FIG. 3. The computing device 1400 may include one or more of each of the following components: a memory 1402, a processor 1404, a display 1406, network interface controller 1408, an input device 1410, and/or an output module 1412.

The memory 1402 includes any non-transitory computer-readable storage media for storing data and/or software that is executable by the processor 1404 and which controls the operation of the computing device 1400. In an embodiment, the memory 1402 may include one or more solid-state storage devices such as flash memory chips. Alternatively, or in addition to the one or more solid-state storage devices, the memory 1402 may include one or more mass storage devices connected to the processor 1404 through a mass storage controller (not shown in FIG. 14) and a communications bus (not shown in FIG. 14). Although the description of computer-readable media contained herein refers to a solid-state storage, it should be appreciated by those skilled in the art that computer-readable storage media can be any available media that can be accessed by the processor 1404. That is, examples of computer readable storage media include non-transitory, volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. For example, computer-readable storage media may include RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, DVD, Blu-Ray or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computing device 1400.

The memory 1402 may store application 1416 and/or data 1414. The application 1416 may, when executed by the processor 1404, cause the display 1406 to present user interface 1418 on the display 1406.

The processor 1404 may be a general purpose processor, a specialized graphic processing unit (GPU) configured to perform specific graphics processing tasks while freeing up the general purpose processor to perform other tasks, a programmable logic device such as a field programmable gate array (FPGA) or complex programmable logic device (CPLD), and/or any number or combination of such processors or devices configured to work independently or cooperatively.

The display 1406 may be touch-sensitive and/or voice-activated, enabling the display 1406 to serve as both an input and output device. Alternatively, a keyboard (not shown), mouse (not shown), or other data input devices may be employed.

The network interface 1408 may be configured to connect to a network, such as a local area network (LAN) including a wired network and/or a wireless network, a wide area network (WAN), a wireless mobile network, a Bluetooth network, and/or the Internet. For example, the computing device 1400 may receive design requirements and predetermined variables and perform the procedure 300 of FIG. 3 to design an antenna assembly. The computing device 1400 may receive updates to its software, for example, application 1416, via the network interface controller 1408. The computing device 1400 may also display notifications on the display 1406 that a software update is available.

In another aspect, the computing device 1400 may receive computed tomographic (CT) image data of a patient from a server, for example, a hospital server, Internet server, or other similar servers, for use during surgical planning. Patient CT image data may also be provided to the computing device 1400 via a removable memory (not shown in FIG. 14).

Input device 1410 may be any device by means of which a user may interact with the computing device 1400, such as, for example, a mouse, keyboard, foot pedal, touch screen, and/or voice interface.

Output module 1412 may include any connectivity port or bus, such as, for example, parallel ports, serial ports, universal serial busses (USB), or any other similar connectivity port known to those skilled in the art.

The application 1416 may be one or more software programs stored in the memory 1402 and executed by the processor 1404 of the computing device 1400. During a design phase for loop antennas, one or more software programs in the application 1416 may be loaded from the memory 1402 and executed by the processor 1404 to automatically design loop antennas, given certain parameters and/or constraints, such as seed shape information, the number of loops in each loop antenna, and/or the like. In some embodiments, during a planning phase, one or more programs in the application 1416 guides a clinician through a series of steps to identify a target, size the target, size a treatment zone, and/or determine an access route to the target for later use during the navigation or procedure phase. In some other embodiments, one or more software programs in the application 1416 may be loaded on computing devices in an operating room or other facility where surgical procedures are performed, and is used as a plan or map to guide a clinician performing a surgical procedure, but without any feedback from the medical device used in the procedure to indicate where the medical device is located in relation to the plan.

The application 1416 may be installed directly on the computing device 1400, or may be installed on another computer, for example a central server, and opened on the computing device 1400 via the network interface 1408. Application 1416 may run natively on the computing device 1400, as a web-based application, or any other format known to those skilled in the art. In some embodiments, the application 1416 will be a single software program having all of the features and functionality described in the present disclosure. In other embodiments, the application 1416 may be two or more distinct software programs providing various parts of these features and functionality. For example, the application 1416 may include one software program for automatically designing loop antennas, another one for converting the design into a CAD file, and a third program for PCB layout software program. In such instances, the various software programs forming part of the application 1416 may be enabled to communicate with each other and/or import and export various data including settings and parameters relating to the design of the loop antennas. For example, a design of a loop antenna generated by one software program may be stored and exported to be used by a second software program to convert into a CAD file, and the converted file may be also stored and exported to be used by a PCB layout software program to complete a blueprint of the loop antenna.

The application 1416 may communicate with a user interface 1418 which generates a user interface for presenting visual interactive features to a user, for example, on the display 1406 and for receiving input, for example, via a user input device. For example, user interface 1418 may generate a graphical user interface (GUI) and output the GUI to the display 1406 for viewing by a user.

In a case that the computing device 1400 may be used as the EMN system 100, the control workstation 102, or the tracking device 160, the computing device 1400 may be linked to the monitoring device 130, thus enabling the computing device 1400 to control the output on the monitoring device 130 along with the output on the display 1406. The computing device 1400 may control the monitoring device 130 to display output which is the same as or similar to the output displayed on the display 1406. For example, the output on the display 1406 may be mirrored on the monitoring device 130. Alternatively, the computing device 1400 may control the monitoring device 130 to display different output from that displayed on the display 1406. For example, the monitoring device 130 may be controlled to display guidance images and information during the surgical procedure, while the display 1406 is controlled to display other output, such as configuration or status information of an electrosurgical generator (not shown in FIG. 1).

The application 1416 may include one software program for use during the planning phase, and a second software program for use during the navigation or procedural phase. In such instances, the various software programs forming part of application 1416 may be enabled to communicate with each other and/or import and export various settings and parameters relating to the navigation and treatment and/or the patient to share information. For example, a treatment plan and any of its components generated by one software program during the planning phase may be stored and exported to be used by a second software program during the procedure phase.

Although embodiments have been described in detail with reference to the accompanying drawings for the purpose of illustration and description, it is to be understood that the inventive processes and apparatus are not to be construed as limited. It will be apparent to those of ordinary skill in the art that various modifications to the foregoing embodiments may be made without departing from the scope of the disclosure. 

What is claimed is:
 1. A computer-implemented method of designing an antenna assembly for radiating an electromagnetic field for electromagnetic navigation, the method comprising: computing, relative to a coordinate system of a substrate having a boundary, a plurality of diagonal lines based on a seed rectangle having a plurality of vertices, respectively, wherein the plurality of diagonal lines bisect the plurality of vertices of the seed rectangle, respectively, and extend from the plurality of vertices of the seed rectangle, respectively, to the boundary; for each of the plurality of diagonal lines: determining a plurality of distances between a plurality of adjacent pairs of planar antenna vertices, respectively, to be positioned along the respective diagonal line, wherein the plurality of distances increase in a direction from the respective vertex of the seed rectangle to the boundary, and positioning the planar antenna vertices along the respective diagonal line based on the determined plurality of distances; and generating a planar antenna layout by interconnecting the planar antenna vertices by way of respective straight linear portions to form a plurality of loops sequentially traversing each of the plurality of diagonal lines.
 2. The computer-implemented method according to claim 1, wherein the plurality of distances are determined based at least in part on a predetermined number of loops of the planar antenna.
 3. The computer-implemented method according to claim 1, wherein the plurality of distances are determined based at least in part on at least one of a predetermined minimum spacing between adjacent vertices or a predetermined minimum spacing between adjacent traces.
 4. The computer-implemented method according to claim 1, wherein the substrate has a plurality of layers and the method further comprises generating a plurality of planar antenna layouts corresponding to the plurality of layers, respectively.
 5. The computer-implemented method according to claim 1, further comprising: adding to the planar antenna layout a plurality of straight linear portions routed from at least two of the planar antenna vertices to a connector location with respect to the coordinate system of the substrate.
 6. The computer-implemented method according to claim 1, further comprising: for each of the plurality of diagonal lines: computing a layout distance between the respective vertex of the seed rectangle and the boundary along the respective diagonal line, wherein the determining of the plurality of distances between the plurality of pairs of adjacent planar antenna vertices, respectively, is based at least in part on the computed layout distance.
 7. The computer-implemented method according to claim 1, wherein each of the plurality of loops includes a plurality of the straight linear portions and a plurality of the planar antenna vertices.
 8. The computer-implemented method according to claim 1, wherein an outermost planar antenna vertex of the plurality of planar antenna vertices is distanced from the boundary of the substrate by not more than a predetermined threshold.
 9. The computer-implemented method according to claim 1, further comprising: exporting data corresponding to the generated planar antenna layout to at least one of a circuit board routing tool or a circuit board manufacturing tool.
 10. The computer-implemented method according to claim 1, further comprising: exporting data corresponding to the generated planar antenna layout to an electromagnetic simulation tool, and simulating, based on the exported data, an electromagnetic field based on superposition of a plurality of electromagnetic field components from the plurality of straight linear portions of the planar antenna layout, respectively.
 11. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform a method of designing an antenna assembly for radiating an electromagnetic field for electromagnetic navigation, the method comprising: computing, relative to a coordinate system of a substrate having a boundary, a plurality of diagonal lines based on a seed rectangle having a plurality of vertices, respectively, wherein the plurality of diagonal lines bisect the plurality of vertices of the seed rectangle, respectively, and extend from the plurality of vertices of the seed rectangle, respectively, to the boundary; for each of the plurality of diagonal lines: determining a plurality of distances between a plurality of adjacent pairs of planar antenna vertices, respectively, to be positioned along the respective diagonal line, wherein the plurality of distances increase in a direction from the respective vertex of the seed rectangle to the boundary, and positioning the planar antenna vertices along the respective diagonal line based on the determined plurality of distances; and generating a planar antenna layout by interconnecting the planar antenna vertices by way of respective straight linear portions to form a plurality of loops sequentially traversing each of the plurality of diagonal lines.
 12. The non-transitory computer-readable medium according to claim 11, wherein the plurality of distances are determined based at least in part on a predetermined number of loops of the planar antenna.
 13. The non-transitory computer-readable medium according to claim 11, wherein the plurality of distances are determined based at least in part on at least one of a predetermined minimum spacing between adjacent vertices or a predetermined minimum spacing between adjacent traces.
 14. The non-transitory computer-readable medium according to claim 11, wherein the substrate has a plurality of layers and the method further comprises generating a plurality of planar antenna layouts corresponding to the plurality of layers, respectively.
 15. The non-transitory computer-readable medium to claim 11, wherein the method further comprises: adding to the planar antenna layout a plurality of straight linear portions routed from at least two of the planar antenna vertices to a connector location with respect to the coordinate system of the substrate.
 16. The non-transitory computer-readable medium according to claim 11, wherein the method further comprises: for each of the plurality of diagonal lines: computing a layout distance between the respective vertex of the seed rectangle and the boundary along the respective diagonal line, wherein the determining of the plurality of distances between the plurality of pairs of adjacent planar antenna vertices, respectively, is based at least in part on the computed layout distance.
 17. The non-transitory computer-readable medium according to claim 11, wherein each of the plurality of loops includes a plurality of the straight linear portions and a plurality of the planar antenna vertices.
 18. The non-transitory computer-readable medium according to claim 11, wherein an outermost planar antenna vertex of the plurality of planar antenna vertices is distanced from the boundary of the substrate by not more than a predetermined threshold.
 19. The non-transitory computer-readable medium according to claim 11, wherein the method further comprises: exporting data corresponding to the generated planar antenna layout to at least one of a circuit board routing tool or a circuit board manufacturing tool.
 20. The non-transitory computer-readable medium according to claim 11, wherein the method further comprises: exporting data corresponding to the generated planar antenna layout to an electromagnetic simulation tool, and simulating, based on the exported data, an electromagnetic field based on superposition of a plurality of electromagnetic field components from the plurality of straight linear portions of the planar antenna layout, respectively. 